®

by Robert L. CannonUpdated and edited byAnn Grimm and Jim Kranich

This booklet is designed to help youunderstand some principles of rocketflight. To get the most from yourstudy, follow these instructions:

Whenever ** appear, stop readingimmediately and answer the question or perform the action which has justbeen suggested. Keep thinking and try to reason out why the action was performed. Try to answer each questionbefore going on with your reading......

This bit of verse was probably one ofthe first things you learned aboutspace. You now know that stars arehuge bodies of extremely hot gases.Stars other than Sol, our sun, are extremelyfar away. Atomic reactions consumetremendous quantities of their matterevery second, yet stars’ masses are sogreat that millions of years go by beforetheir sizes are significantly reduced.

The early astronomers named many ofthe stars. Eventually, some noticedthat certain ‘stars’ did not stay where they belonged in the sky. These migrants were named ‘planets’ (wanderers).

There are nine of the ‘wanderers’ orplanets that have been discovered in our solar system.. Telescopes (including the Hubble Space Telescopein Earth orbit) and mathematics haveenabled modern astronomers to alsoidentify and study numerous moonsaccompanying the nine planets. In addition to these nine planets andtheir moons, thousands of asteroidsand a number of comets revolve in orbits around the sun.

... An object in motion will continue in motion at a constant speed in astraight line as long as no unbalanced

force acts upon it.

An object in space near another objectis influenced by the gravitational fieldof the other object. For example, the moon is attractedtowards Earth by the Earth’s gravita-tion. Mathematically, the gravitationalattraction that two objects have foreach other is as follows:

As can be seen from the formula, asthe mass of either object increases, so does the gravitational forcebetween them. As the distancebetween both objects increases, the gravitational force decreases.

Theforce of

the Earth’sgravity pulls

the moon toward Earth as the moonrevolves about Earth. In effect, themoon is falling toward Earth. The moon’s motion also causes themoon to move laterally (sideways) atthe same time. The moon’s velocity isjust enough to keep it falling towardEarth at the same rate that the Earth’scurvature causes the Earth’s surface tobecome farther from the moon.

2

NEWTON’S FIRST LAW OF MOTION:

“Twinkle, twinkle, little star.How I wonder what you are;Up above the world so high,Like a diamond in the sky.”

d

F

Earth MoonF=

G x M x m d2

Objects at rest will stay at rest and objects in motion will stay in motion in a straight line unless acted upon by an unbalanced force.

ORBITPRODUCINGFORCES

WHY SATELLITESSTAY IN ORBIT

F= the gravitation force between thetwo objects

M= the mass of one object (Earth)m= the mass of another object (Moon)d= the distance between both objects’

center of massG= gravitation at constant

If your Estes rocket werelaunched deep into space whereatmosphere (drag) and gravity(unbalanced forces) could notaffect it after engine burnout,it would travel a straight line at a constant velocity forever!

Moon’s actual motion asinfluenced by Earth’sgravity.

Earth

Moon

Moon’s motion if not affected byEarth’s gravity.

Due to the distance between theEarth’s surface and center of mass, weexperience a gravitational accelerationof 9.81 meters per second per sec-ond(9.81 m/s2) or 32.2 feet per second per second (32.2 ft/s2). This means that a free falling objectstarting from an initial velocity ofzero, will gain speed at the rate of32.2 ft/s for each second of travel.

For the first second of free fall, an object will travel approximately 16 feet. The Earth’s surface curves“down” 16 feet in about 5 miles.Therefore, an object moving“horizontally” at 5 miles per secondwill fall at a rate which keeps it at aconstant distance above the Earth’ssurface. This situation produces anobject which is a satellite of Earth and has a circular orbit.

Mathematically, the expression whichcalculates the velocity needed tomaintain a circular orbit around Earthis as follows:

V= (u/r)1/2

where, r is the distance between thesatellite and Earth’s center (center ofmass) and u is the Universal Constant(Gravitational Constant times the Earth’s mass).

The velocity which a satellite musthave to go into a circular orbit nearthe Earth’s surface is about 5 miles per second. This is about 18,000 miles per hour (5 miles/second x 60 seconds/minute x 60 minutes/hour).To reach this high speed, artificial(man-made) satellites must belaunched by very powerful rockets.

Should an object receive a greatervelocity than required to maintain a circular orbit, even if launched in the proper direction, it will not stay in a circular path. It will insteadgo into an elliptical orbit or escapeentirely if the velocity is great enough.

If theobject doesnot reach ahighenoughvelocity togo into cir-cular orbit,it will fallback toEarth.

The farther an object is from Earth, the weaker is the force with which the Earth’s gravitation pulls on theobject (remember the earlier equationthat shows the gravitational forcebeing inversely proportional to thesquare of the distance?!).

Since this is true, the higher an object isabove the Earth’s surface, the slower is itsrate of fall due to the Earth’s gravity. Sincethe object tends to fall at a slower rate thehigher it is, it follows that the farther anobject is from Earth, the slower it will haveto move to stay in orbit.

A satellite which is in orbit far aboveEarth has a very long orbital path andis moving relatively slowly. The satel-lite has a very long period (the timerequired to make one revolution).

A satellite in a lower orbit has a shorter orbital path. As can be seenfrom the circular orbit and gravitation-al attraction equations, the satellitemust be moving faster since the gravi-tational attraction is greater due tothe closer proximity with the primary. If the actual velocity of the satellite isnot increased accordingly for the loweraltitude, it will fall out of orbit and re-enter the Earth’s atmosphere. These factors cause the satellite tohave a fairly short period.

3

Trajectory of anobject which “falls” too fast.

CircularOrbit

Orbit set up byan object whichdoes not “fall”fast enough toremain in circular orbit

C

The moon’s velocity is just great enoughto carry it farther away from Earth alongpath AB in a certain time during which itfalls toward Earth a distance BC

Moon’s Position At a Given Moment

A B

Motion as influencedby Earth’s gravity

Point onEarth’ssurfacedirectlybelow A

Point on Earth’ssurface directlybelow B

Distancemoon “falls”because ofthe Earth’sgravity as itmoves fromA to C

Distance Earth’ssurface “drops”below horizon line

Satellite

Primary

Satellite (an object in spacerevolving about anotherbody in space)

Orbit (path of thesatellite as itrevolves aboutthe primary)

The Moon(Luna) is asatellite ofEarth (Terra)

Orbit

Low Orbit: High orbital velocity, small orbital path

High Orbit: Low orbital velocity,large orbital path

Man-made satellites are placed inorbits of varying altitudes dependingupon the purpose of the satellite.Some are close to the Earth to makedetailed observations and some areplaced in very high orbits which will remain in orbit for long periods of time.

From the velocities and periods chart,you can see that one particular orbithas a period of 24 hours. It makesone revolution about the Earth every24 hours. The Earth also rotates aboutits own axis once every 24 hour hours.This results in the satellite remainingin a fixed position above the Earth andis referred to as a “GeosynchronousOrbit”. Communication satellites areplaced into this type of orbit to provide continuous communicationcoverage for that section of Earthbelow it.

Why would a satellite placed in a verylow orbit close to the Earth, less than200 miles, not stay in orbit for many months?

* *

You can answer this question yourself.Let’s pretend that you want to throw abaseball into orbit. You probably realize that your chances of successaren’t too great!! However, let’s goahead and try. You can go outside and try this if you wish, but let’s gothrough the reasoning together first.

If you throw the ball as high and asfar as you can, you don’t have much ofa chance of getting the ball into orbiteven if you are very strong. Why not?

* *You could

not throwthe ballwithenough

energy to reachescape velocity (the

minimum velocity thata moving object must

have to leave thevicinity of Earthand not return).

The ball was pulled toward the center of the Earth by the force of gravity.

Could you tell that the ball was slowing down as it went upward? It was.

Try this experiment in some openplace. Throw the ball as nearly vertical (straight up) as you can.Watch the ball as it goes up and comes down. If you have trouble seeing the ball well and concentratingon observing its motion, have a friendthrow it while you stand to the sideand observe.

* *

MOMENTUMThe ball starts slowing down theinstant it leaves your friend’s hand. At the moment the ball leaves thehand, it has a certain velocity upward.The energy given to the ball by throw-ing it caused the ball to have a certainamount of momentum at the point ofhand release. The amount of momen-tum possessed is calculated by multiplying the ball’s mass times the ball’s velocity.

MOMENTUM = MASS x VELOCITYMass is a property that all objects possess and is a measurement of that object’s resistance to a change inmotion. Because of the gravitationalattraction on Earth, we commonly usethe term weight instead of mass. The more massive the object, the moreit weighs on Earth and obviously heavier objects are more difficult tomove. However, in space objects areweightless yet they still possess mass.In this weightless condition, objectswith more mass are more resistant to a change in motion. It requires moreforce to change the motion as compared to a less massive object.

On Earth we can simply note thatweight depends on mass, so thegreater the mass of something, the more it will weigh.

The ball’s mass doesn’t change whenyour friend throws it up into the air,yet the ball soon slows down to acomplete stop, then starts falling downto the ground. Can you observe any

4

VELOCITIES AND PERIODSEARTH SATELLITES IN CIRCULAR ORBITS

AT VARIOUS ALTITUDES

AltitudeMiles

0 1 hr. 24 min.

1 hr. 28 min.

1 hr. 38 min.

4 hr. 47 min.

24 hr. -----

4.92

4.85

4.68

3.27

1.91

100

400

5,000

22,300

VelocityMiles per sec. Period

Even “Atlas”has problems...

pattern to the speed with which theball falls?

* *

As the ball starts falling from the momen-tary pause at the top of its path, itfalls faster and faster. This is caused bythe force of gravity pulling it downward.

Your attempt to throw a ball into orbit around the earth didn’t work. The moment the ball left your hand, it had only so much kinetic (motion)energy with which to go into orbit.The force of gravity was pulling theball downward all the time, but fromthe instant the ball left your hand youcould not supply force to the ball tocounteract the force of gravity. Theforce of gravity pulled downward whilethe ball was moving upward. Result -the ball was slowed down. Was theforce of gravity the only force actingon the ball once it left your hand?

* *

DRAGNo. The ball moved through the air, and the air produced drag on the ballto slow it down. This drag is theresistance the air presents to themovement of the ball through the air. You have felt this drag as you ran on a calm day and felt the wind in yourface or as you rode your bicycle. The faster an object is moving throughthe air, the greater is the aerodynamic(moving air) drag on it.

The force of gravity on the ball wasthe same regardless of the speed with which you threw the ball. The amount of drag encountered

depends upon the speed. Both forcesacted to reduce the ball’s upwardmomentum. The force of gravitypulled the ball back to earth.

Your Estes rocket encounters the sameforces during flight as did the ball.When the engine burns out, the rockethas a certain amount of momentum.The forces of gravity and drag slow therocket down as it coasts upward andeventually stops and starts comingdown. What would your Estes rocketdo after engine burnout if there wasno atmosphere or gravity?

* *

Without gravity or air (producing drag)to reduce the rockets momentum, it would behave according to Newton’sFirst Law of Motion and continue inmotion, in a straight line, at constantvelocity unless an unbalanced forceacted upon it. In short, it wouldcoast upward forever!What forces exist on a satellite in orbit far above the Earth?

* *

The gravity of Earth is present, ofcourse, although it is not very strongfar from Earth. The closer the satelliteis to Earth, the stronger is the force of gravity acting on it. Rememberfrom the gravitational force equation,the force of gravity is inversely proportional to the square of the distance between the centers of massof both objects. In other words, thesame satellite twice as far away (from the Earth’s center) would beattracted only 1/4 as strongly.

As we go farther from the surface ofour planet, the atmosphere gets thinner.Yet there is a measurable amount of aireven at an altitude of 1,000 miles up.The air resistance eventually slows thesatellite down below that required for

a circular orbit (refer to the circularorbit equation). This condition, combined with the Earth’s gravity,causes the satellite in low orbit to soon“fall” out of orbit and return to Earth.Satellites in extremely high orbitsencounter much less drag and lowergravity, so they will remain in orbit for very long periods of time.

INERTIAInertia is the tendency of a body atrest to remain at rest unless pushed or pulled by an unbalanced force, and a body in motion continues tomove in the same direction at thesame speed unless acted upon by an unbalanced force.

This definition is not as complicatedas it sounds. Many people refer to twotypes of inertia. One kind, which wemay call static inertia, is the inertiapossessed by non-moving bodies. Can you think of an example of this?

* *

A book sitting on a desk is one goodexample. As long as no unbalancedforce acts on the book to move it,the book stays where it is. Can youthink of a way to move the book?

* *

Any force, applied to the book in greatenough quantity, will cause the bookto move. Picking up the book, push-ing it along the desk with your finger,or hitting the book hard enough to knock it off the desk all qualify asforces great enough to move it.

5

LOW SPEED - LOW DRAG

HIGH SPEED - VERY HIGH DRAG

An unbalanced force is onewhich changes motion.

Another kind of inertia is the inertiapossessed by a moving body, some-times called kinetic inertia. This is the tendency for a moving body tokeep moving once in motion.

Let’s consider again a satellite in orbitfar above the Earth. The force of gravity, while weak, still pulls on thesatellite. The satellite still encounterssome aerodynamic drag from the fewatoms, molecules and ions of theatmosphere present this high abovethe surface. However, this aero-dynamic drag force is very small.

The satellite may weigh very little if it is in a weak gravitational field.However, the satellite has the samemass when in orbit as it did when on the ground.

The kinetic energy possessed by thesatellite due to its motion is equal tothe product of 1/2 the mass of thesatellite times the square of its velocity. Due to its kinetic inertia the moving satellite tries to travel in a straight line. Result - the satellite’skinetic inertia tries to keep it movingin a straight line at a tangent awayfrom its position in orbit.

An interesting way to experiment with objects revolving about a point in space is to conduct the followingexperiment. Obtain a thread spool(preferably empty), a long piece ofstring (about four feet [122 cm]), anda lightweight object (small rubber ball,eraser, or the like). Tie the objectsecurely to one end of the string. Pass the other end through the hole in thespool and pull the string through as faras possible without breaking the string.Stand in an open area and hold the

spool above your head with one hand.Hold the string with the other hand.Allow the object to pull about one foot(30.5 cm) of string through the spoolbefore stopping the string’s movementwith the other hand. Start whirlingthe object about the spool.

Feel the force with which the objectpulls on the string. Whirl the objectfaster. Notice how the pull becomesgreater.

* *Moving objects possess momentum.The amount of momentum an objecthas is determined by multiplying itsmass times its velocity. For example, a100 pound (mass) satellite moving at4.85 miles per second (orbital velocityfor a satellite in circular orbit at aheight of 100 miles above the Earth’ssurface) will have a momentum of2,560,800 foot-pounds/second (100lbs.x 4.85 miles/second x 5280 feet/mile).Similarly in the metric system of measurements, a 45 kilogram (kg)satellite moving at 7790 meters/second (m/s) will have a momentum of 350,550 kg-m/s.

The inertia a moving body possessestries to keep it moving in a straightline at a constant velocity. The objectyou are whirling is attempting to go ina straight line, but the string exerts acontinual force on the object causingit to move in a circular path.

The whirling object and spool may becompared to a satellite and Earth. Thestring represents gravity, the whirlingobject is the satellite and Earth is thespool. This is a model of the real situ-ation, although not an accurate one.

What would happen to the objectrevolving about the spool if you wereto suddenly release the string? Thiscompares to what inertia would do toan artificial satellite if Earth’s gravitysuddenly ceased to exist.

* *

By whirling the object faster or slowerand by changing the length of thestring, a number of interesting experiments are possible. This canhelp you get a “feel” for understandingthe forces at work on a satellite in orbit.

One example which can be performedis to keep the pull on the string reasonably constant while measuringthe period of revolution for a shortlength of string (low orbit) as compared to the period of revolutionfor a much longer length of string.

6

Inertia causes an object to proceed at a

constant speed in a straight line.

SIMULATION OF

ORBITAL MOTION

SNAP!!

Section I

Read each statement and decidewhether it is True or False (write T or F).

______ 1. All satellites are man made.______ 2. Gravity has no effect on

satellites in orbit.______ 3. As we go farther from the

Earth the atmosphere gets thinner, but,there is a measurable amount of air even at an altitude of 1000 miles.

______ 4. An unbalanced force is one that does not change motion.

______ 5. The speed at which a body passes through the airhas no effect on the amount of drag produced.

______ 6. The mass of a satellite changes as its distance from Earth changes.

______ 7. A satellite has inertia.______ 8. A satellite actually falls

around the Earth.______ 9. Satellites placed in higher

orbits remain in orbit for longer periods of time than those placed in lower orbits.

______10. Momentum is the only major force acting on a satellite.

______11. A satellite in a high circular orbit has a higher orbital velocity than one in low orbit.

______12. The ‘period’ of a satellite refers to its time in orbit before falling.

______13. “Escape velocity” refers to the force necessary to lift a satellite off the Earth’s surface.

______14. An object which is in motion continues in motionat different speeds unless an unbalanced force acts upon it.

______15. For any one specified altitude of a satellite in a circular orbit, there is only one specific velocity it must maintain.

______16. You would weigh less on top of Mount Everest (high-est mountain in the world) than you would in Death Valley (lowest elevation on and in the world).

Section II

Multiple choice. Circle or underline the best word orwords to complete each statement.

17. The inertia possessed by nonmoving bodies may be called (kinetic, constant, static) inertia.

18. The velocity which a satellite must have to go into circular orbit near the Earth’s surface is about (22,300, 18,000, 50,000) miles per hour.

19. The moon is attracted toward earth by the (gravity, magnetic force, solar energy) of the earth.

20. There are (eleven, nine, thirty) planets in our solar system.

21. The force acting on a satellite which keeps it in orbit is (trajectory, orbital, gravity) .

22. The resistance that results when a body is moved through the air is called (drag, thrust, lift).

23. The momentum of a body moving through the air is measured by multiplying (force, height, mass) times velocity.

24. The path followed by a satellite moving around the Earth is called its (vertigo, orbit, trajectory).

25. The time that it takes a satellite to make one revolution around the Earth is called its (segment, particle, period).

26. The velocity required by a space craft to leave orbit and head for the moon is called (separation, escape, momentum) velocity.

7

REVIEWNEWTON’S FIRST LAW OF MOTION

This section is designed to helpyou better understand someideas which are important torocketry and model rocketry.Follow the instructions carefully.

You will need a penciland a strip of cardboard orthick paper that is four inches wide and ten inches long. Place this stripover the next column and move thepaper down until it comes to the firstdotted line. Study the material, thenfill in the blank(s).

Move the paper down to uncover theanswer and check your response. Your answer does not need to be in the exact words given as long as it expresses the correct idea. If your response was incorrect, reviewthe material, correct the answer andmove on to the next paragraph. Follow these steps throughout this section.

The previous section (Newton’s FirstLaw) examined the condition whenunbalanced forces were not present.That is commonly referred to as a static condition; no acceleration. An unbalanced force is a force which is not matched by an opposing force.Let’s examine the effect when unbalanced forces exist which causeacceleration (a change in velocity) creating a dynamic condition.

Mathematically, Newton’s Second Lawis expressed as follows:

If we had a static situation (accelera-tion is zero), the right side of theequal becomes zero. The net sum ofthe forces then equals zero too. This shows that we have no unbal-anced forces. In a dynamic situationwhere unbalanced forces are present(net sum of all forces not equal tozero), the quantity m x a, has an actualvalue indicating the object of mass m will accelerate by the amount a.

You can see that the amount of accel-eration is directly proportional to themagnitude of the unbalanced forces;the greater the force, the greater theacceleration. The magnitude of theacceleration is also inversely propor-tional to the amount of mass resisting

the motion; the greater the mass, thelower the acceleration.

If a football player charges into another player who is not expectingthe charge, the player who is hitreceives an unbalanced force. Heprobably gets knocked several feet!

If you hold an object at arms lengthand release it, what happens? The object _______.———————————————

Any time the speed at which an objectis moving is changed,the object isaccelerated. If the object ismade to moveat a greaterspeed, we saythat the objectreceives positiveacceleration.Conversely, amoving objectthat is sloweddown wouldundergo negative acceleration(deceleration).

8

NEWTON’S SECOND LAW OF MOTION:

UNBALANCED

FORCES AND

ROCKETS

Force is equal to mass times acceleration.

where: F = force (newtons or pounds)m = mass (kilograms or slugs)a = acceleration

(m/s2 or ft/s2)

F = m x afalls

ACCELERATION

An unbalanced force acting on anobject causes the object to____________.———————————————

When you release the object you wereholding, it receives ___________ accel-eration because of the force of______________.———————————————

To properly describe a force we need toknow the magnitude (amount) of theforce and the direction in which theforce is acting.

An unbalanced _____________ accelerates an object in the direction in which the ____________ is acting.———————————————

The harder you throw a ball, all otherfactors being constant, the farther itwill go. When you throw the ball withonly a little force, the ball receivesonly a small acceleration. If you throw the ball as hard as youcan, it receives a large acceleration.

A large force produces a __________acceleration than a smaller force on the same object.———————————————

A larger acceleration produces a___________ speed change than a small acceleration for the same length of time.———————————————

All moving objects possess momentum.The momentum of a moving object isdetermined by multiplying the massof the object (its quantity of matter)times the velocity (speed in a certaindirection) of the object.

MASS x VELOCITY = MOMENTUM

Which has more momentum, a ball mov-ing at a given velocity or an identicalball moving at a higher velocity? Theball moving at the ___________velocity has a greater momentum.————————————————

The greater the unbal-anced force acting on anobject, the greater isthe acceleration theforce produces. The forwardforce a rocket engine creates iscalledthrust.

Which rocket will accelerate more if theindividual engines produce equal thrustand the rockets have equal total mass-es? Rocket _______ will acceleratemore than the other rocket.————————————————

The more massive an object is, thegreater is the force needed to achievea given acceleration (rate of velocity

change). In other words, agiven force will accelerate anobject of low mass more than

it would accelerate anobject of greater mass.

The engines of rocketsC and D produce thesame thrust. Rocket Chas much more massthan Rocket D.Rocket _______ will

have a greater accelerationthan the other rocket.

————————————————

A rocket engine can produce a certain amount of thrust. To cause asatellite to reach the desired velocity,the rocket must accelerate the satellitefrom zero velocity to the desired velocity.

The entire rocket (satellite, engine,propellant, body, etc.) is acceleratedby the engine’s thrust.

The total momentum achieved by arocket is equal to the total momentumachieved by the rocket’s exhaust gases.As we have learned, momentum equalsmass times velocity. The exhaustgases of an Estes rocket have lowmass, but their velocity is extremelyfast. Because the total momentum isthe same, a rocket having mass greaterthan the exhaust gases will achieve avelocity lower than the exhaust gases.

9

AB

C

D

ACTION REACTIONaccelerate

positivegravity

forceforce

larger

greater

higher

A

D

MOMENTUM

THRUST

3rd

2nd

StageEngine

1st

If the same thrust is applied to a rocketof small mass as to one of greatermass, which will achieve a higheracceleration - the smaller mass orgreater mass rocket?————————————————

If Newton’s second law of motion isrewritten as F/m=a, it is apparentthat reducing a rocket’s mass which anengine’s thrust must accelerate willenable the rocket to achieve greateracceleration. This results in the rocketattaining higher velocities.

The less the total mass of the rocket,the __________ the velocity the payload can reach when the rocket’sengine is operated for a specified time.————————————————

The mass of a satellite does notchange as it moves from its positionatop a rocket on the launch pad toachieving orbit. Since the satellitehad zero momentum (its mass timeszero velocity equals zero momentum)on the launch pad but a large momen-tum as it follows its orbit, the satellitehas undergone a tremendous change inits momentum. The momentum possessed by all objects on Earthbecause of the Earth’s motion is notcovered in this booklet.

A small engine producing a smallthrust but operating for a long periodof time can make a given payload massreach a high velocity (assuming thethrust is greater than the rocket’sweight and drag combined). This is the principle of impulse which isderived from Newton’s second law. For those with the appropriate mathand physics background, the derivationis as follows:F = m x a Newton’s second law

a (acceleration) isthe first derivative of

velocity with respect to time

F dt = m dv multiplying bothsides of the equation by dt

F ∆t = m ∆v a derivative repre-sents a change, ∆

Σ F ∆t = m(vf - vi)The sum of all forces times the length of time they act is equal to the mass of the object times the change in velocity. Initial velocity is vi

and the final velocity is vf.

The left side of the equation representsimpulse (force times time) and theright side represents momentum (masstimes velocity). This equation showsthat the sum of all impulses is equal tothe change in momentum. Because oursmaller engine operated for a longerperiod of time, the rocket was able toreach greater velocities. A larger engineproducing greater thrust could make thesame payload mass reach the samevelocity by operating for a __________period of time.————————————————

A small rocket engine producing asmall thrust may not be able to lift arocket with the payload and the neces-sary propellant, so a large engine or acluster of small engines are often necessaryto lift the rocket off the launch pad.

As the rocket’s

engine operates, thepropellant is converted to

gases which leave the rocket whichreduce the rocket’s mass. As a result, a steady thrust level can produce an

_______ in the rockets acceleration.

The greater the mass of a rocket, the_______________ is the accelerationproduced for a given total thrust.———————————————

As the propellant ineach stage of amulti-stage rocket isused, that stage canbe dropped. Thisreduces the mass of therocket (by removing theengine and other parts ofthat stage). As a result, thethrust of the next stage’s enginepushes a smaller mass. This allowsthat engine to give the rocket moreacceleration than it could were therocket more massive. It also allowsthe engine’s thrust to be reduced tomaintain the current velocity. Thispermits the engine to operate longerusing a given amount of fuel to reacha higher altitude.

As a rocket’s stages separate from therest of the rocket, the rocket’s totalmass ______ .————————————————

Staging allows a payload to reach a _______________ velocity for a specific mass of propellant than wouldbe achieved by using only a single-stagerocket.————————————————

F = m

10

greater

shorter

increase

lower

decreases

greater

The smaller mass rocket

THRUST

MULTI-STAGED

ROCKETS

dvdt

Section IRead each statement and decidewhether it is True or False (write T or F).

______ 1. The momentum of a mov-ing object is determined by multiplying the mass of the object times its weight.

______ 2. An unbalanced force is a force which is balanced by an opposing force.

______ 3. A moving body that is slowing down while moving in the positive (forward) direction undergoes negative accel-eration (deceleration).

______ 4. The greater the unbal-anced force acting on an object, the greater the accelera-tion the force produces.

______ 5. When the first stage of a multi-stage rocket is jet-tisoned, the result is thereduction in the mass of the rocket.

______ 6. If equal thrusts are applied to rockets of small mass and large mass, the large mass rocket will receive more acceleration.

______ 7. Using C6-0 and C6-7 engines in a multi-stage rocket, the greatest acceleration is reached with the upper stage.

______ 8. The total mass of a rocketis reduced as the engine operates.

______ 9. Two identical rockets are launched using different engines. At burnout, rocket A has a greater velocity than rocket B. Rocket B has greater momentum and will coast for a longer time than rocket A.

______ 10. A rocket weighing 16 ounces is launched with an engine producing 9 ounces of thrust. The unbalanced forces will cause acceleration in thepositive direction allowing the rocket to lift off the launch pad.

Section II

Multiple choice. Circle or underline the best word orwords to complete each statement.

11. As a rocket’s stage separates from the rest of the rocket, the rocket’s total mass (increases, decreases, stays the same).

12. A large acceleration produces (less, some, more) speed change than a small accelera-tion during the same length of time.

13. A force which is not matched by an opposing force is called an (balanced, stable, unbalanced) force.

14. Any time the speed at which an object is moving is changed,the object is (stopped, rotated, accelerated).

15. The total momentum achieved by a rocket is equal to the total momentum achieved by the rocket’s (engine strength, exhaust gases, electrical charge).

16. If the same thrust is applied to a small mass rocket as to a large mass rocket, the (large, small, circular) mass will receive more acceleration.

17. The less the total mass of the rocket, the (greater, less, same)the velocity the payload can reachwhen the rocket’s engine is operated for a specified time.

18. Mass times velocity equals (acceleration, gravitation, momentum).

19. Force multiplied by a change in time equals (velocity, impulse, thrust).

20. Because the top stage of a multi-stage rocket is traveling at extremely high speeds, this stage can burn for a longer period of time by operating at (higher, lower, the same) thrust than the previous stage.

11

REVIEWNEWTON’S SECOND LAW OF MOTION

Whenever * *appear, stopreading imme-diately and per-form the action which has just beencalled for. Keep thinking and try to reason out why the action was per-formed as well as what happened when the action was performed. Try to answer each question beforegoing on with your reading.

Remember when you were playingbaseball and someone pitched to you?When you hit the ball solidly with thebat, you caused the baseball to reversedirection and begin traveling rapidly inthe other direction. This required a lotof force. You supplied the force byswinging the bat.

Let’s analyze what happened. Whenthe pitcher threw the ball he used alot of force. This force gave the ballmomentum. The momentum dependsupon the mass and the velocity (speed)of the moving body. Therefore, themomentum of the baseball dependsupon the mass of the baseball and the velocity at which it is thrown.

The amount of force with which you hit the ball depended upon themomentum of your bat. The bat’s massremains constant unless you break offpart of the bat or add something to it.The only way to change the momentumof the bat is to change its velocity.

The faster you swung the bat, themore momentum it had. If your bathad more momentum than the ball, theball’s momentum was overcome by thebat’s momentum and the extra momen-tum still possessed by the bat wasimparted to the ball. Since the balland bat were moving in opposite direc-tions, the ball’s direction was reversed.

If the bat shouldhit the ball with less

momentum than the ballpossesses, the bat would be

knocked out of the way. If the bat and ball had exactly equalmomentum, each would rebound offthe other after contact.

Does a rocket’s engine push against the air to make the rocket move? Let’s try some experiments which may answer this question.

You will need two objects. One object is your index finger, the other a cleared area on the top of a strongdesk or table.

Place your index finger on the centerof the cleared space on the table.

Gently push upon this spot.

* *

... Now push harder.

* *

... Push even harder.

* *

Is the table pushing back? Push still harder. Don’t break your finger or the table!

Is the table pushing back yet? If it isn’t, why doesn’t your finger go through the spot on the table? If you exert a force (action) on thetable, the table will push back on yourfinger. The momentum of the ball hitting the bat produced a reactionagainst the action of the bat. What would be the reaction to theforce applied by your finger?

* *

If the force you applied with your fin-ger was the “action”, then the reactionwould be the table’s resistance to thisforce. What would happen if youapplied more force with your fingerthan the table could withstand?

* *

12

WHAT ROCKETSPUSHAGAINSTIN SPACE

NEWTON’S THIRD LAW OF MOTION:For every action there is an equal and opposite reaction.

When the force applied is greater thanthe force with which the object canresist without motion, part of the forcebeing applied will produce motion.When you apply more force with yourfinger than the force with which thetable can react, the finger will dent orpunch a hole in the table or the tablewill move. Since every action alwaysproduces an equal reaction, an equalamount of force is present in both the action and the reaction.

If the table should react against theforce applied by the finger with a force greater than the force applied by the finger, this could open up new areas of study.

If you have difficulty with the ideathat for every action there is an equalreaction in the opposite direction, trypushing your hands against themselvesin front of you. When the muscles ofyour arms push your hands togetherequally hard, no motion occurs. If the right hand is made to pushharder than the left hand, acceleration occurs as both hands moveto the left. However, the reaction force experienced by the left hand will be equal to the force exerted by the right hand.

All these experimentshave been performed tohelp show that for every action thereis an equal but opposite reaction. In a rocket, the action comes as therocket is pushed by the escaping gases

either produced by the chemical reac-tion of the fuel and oxidizer combiningin the combustion chamber, or thecombustion of a solid propellant as in your Estes rocket.

The sides of the combustion chamberprevent the gases from escaping side-ways. The gases cannot escape for-ward since the combustion chamberwill not let them. The only opening tothe outside is the nozzle. Rememberthat a tremendous volume of hot gasesis produced as the fuel is burned.These hot gases have mass and thismass can escape only through therocket’s nozzle at high velocity. Thismeans that the gases have a largemomentum (the mass of the gasestimes the velocity of the gases).

The escaping gases acquire momentumdue to the action. The reaction givesmomentum to the rocket which isequal but opposite in direction. The large mass of the rocket is given a small velocity so that the momentum(reaction) of the rocket is equal to themomentum (action) of the escaping low-mass, high-velocity gases. The unbalanced pressure in its owncombustion chamber is what pushes a rocket through space.

Another activity you can do to demon-strate this principle involves turningyourself into a rocket. For this activityyou will need a heavy weight (10 to 20pounds - a concrete block will do) anda playground swing. Sit in the swing,holding the weight in your lap and pullyour feet up off the ground so you arehanging freely. Without touching anything but the weight and theswing, throw the weight away fromyou, straight forward, as hard as youcan. Be careful you don’t hit someone

with it or fall off the swing. What happened?

* *

You and the swing moved in one direction while the weight moved inthe opposite direction. Which movedfaster - you or the weight?

* *

The weight moved faster than youbecause it had less mass than you.What were you pushing against whenyou started moving?

* *

The weight you were pushing againstcan be compared to the exhaust gasesof a rocket. Your hands on the weightserved the same purpose as the forward wall of the combustion chamber in a rocket. The muscles inyour arms did the same job that thechemical reaction of fuel and oxidizerperforms in a rocket - getting the“exhaust” moving. We can see that a rocket in space “pushes” against itsexhaust gases.

This same experiment can be conduct-ed using a skateboard and weight.

13

Action

Reaction

®A8-3ENGINE

REACTION ACTION

REACTION

ACTION

Section I

Read each statement and decidewhether it is True or False (write T or F).

_____ 1. For every action, there is an equal and opposite reaction.

_____ 2. Exhaust gases from a rocket engine push against the atmosphere to cause the rocket to move.

_____ 3. Rocket engines operate on the moon because of the atmosphere on the moon.

_____ 4. Any force applied always results in a reaction.

_____ 5. When pushing on a table with your finger, no reac-tion from the table results because the table is an inanimate object.

_____ 6. The amount of force applied determines the amount of resulting reaction.

_____ 7. Momentum can be the result of an applied force.

_____ 8. In a rocket engine, the force expelling the escap-ing gases can be consid-ered the action, and the reaction causes the motion of the rocket.

_____ 9. In a rocket engine, the reaction is always greater than the action.

_____10. The rocket engine is limited to operation in the belt of atmosphere surrounding the earth.

Section II

Multiple choice. Circle or underline the best word orwords to complete each statement.

11. Momentum depends upon the (surface, mass, texture) of the moving body and the velocity of the moving body.

12. In a rocket engine the (reaction, action, motivation) comes from the escaping gases.

13. The sides of the (rocket engine, launch rod, combustion chamber) prevent the gases from escaping sideways.

14 In rockets, the escaping gases acquire momentum due to the action, the (thrust, velocity, reaction) gives momentum to the rocket which is equal but opposite in direction.

15. The (balanced, unbalanced, forward) pressure in a rocket’s combustion chamber pushes it through space.

14

REVIEWNEWTON’S THIRD LAW OF MOTION

15

NEWTON’S

FIRST LAW

OF MOTION

1. F2. F3. T4. F5. F6. F7. T8. T9. T

10. F11. F12. F13. F14. F15. T16. T17. static18. 18,00019. gravity20. nine21. gravity22. drag23. mass24. orbit25. period26. escape

NEWTON’S

SECOND LAW

OF MOTION

1. F2. F3. T4. T5. T6. F7. T8. T9. F

10. F11. decreases12. more13. unbalanced14. accelerated15. exhaust gases16. small17. greater18. momentum19. impulse20. lower

NEWTON’S

THIRD LAW

OF MOTION

1. T2. F3. F4. T5. F6. T7. T8. T9. F10. F11. mass12. action13. combustion chamber14. reaction15. unbalanced

REVIEW ANSWERS

Estes rockets operate under Newton’s Three Laws of Motion the same as full scale rockets.Understanding these laws will help you better understand the operation of your Estes rocket as well as enable you to gain a better insight into the behavior of rockets and satellites.

The author expresses gratitude to Dr. Mario Iona, Department of Physics, University of Denver (CO) for numerous constructive suggestions.

NEWTON’S LAWS OF MOTIONAND MODEL ROCKETRY

by Robert L. Cannon

Updated and edited by

Ann Grimm and Jim Kranich

Estes Industries

1295 H Street

Penrose, CO 81240

© Copyright 1972, 1979 & 1998 Centuri Corporation.

All rights reserved

EST 2821

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